Each of the following functions has at most one critical point. Graph a few level curves and a few gradiants and, on this basis alone, decide whether the critical point is a local maximum (MA), a local minimum (MI), or a saddle point (S). Enter the appropriate abbreviation for each question, or N if there is no critical point. 1. f(x, y) =e-3x²-4y² Type of critical point: 2. f(x, y) e³x²-4y² = Type of critical point: 3. f(x, y) = 3x² + 4y² + 4 Type of critical point:
Each of the following functions has at most one critical point. Graph a few level curves and a few gradiants and, on this basis alone, decide whether the critical point is a local maximum (MA), a local minimum (MI), or a saddle point (S). Enter the appropriate abbreviation for each question, or N if there is no critical point. 1. f(x, y) =e-3x²-4y² Type of critical point: 2. f(x, y) e³x²-4y² = Type of critical point: 3. f(x, y) = 3x² + 4y² + 4 Type of critical point:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Each of the following functions has at most one critical point. Graph a few level curves and a few gradiants
and, on this basis alone, decide whether the critical point is a local maximum (MA), a local minimum (MI), or a
saddle point (S). Enter the appropriate abbreviation for each question, or N if there is no critical point.
-3x²-4y²
= e
1. f(x, y)
Type of critical point:
2. f(x, y) = e³x²—4y²
Type of critical point:
3. f(x, y) = 3x² + 4y² + 4
Type of critical point:
4. f(x, y)
=
3x + 4y + 4
Type of critical point:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F937c5b24-3686-40bc-8921-1d1fed2f5241%2Fc831ce33-1660-4609-bdbb-206e5dabd340%2Fukluhnn_processed.png&w=3840&q=75)
Transcribed Image Text:Each of the following functions has at most one critical point. Graph a few level curves and a few gradiants
and, on this basis alone, decide whether the critical point is a local maximum (MA), a local minimum (MI), or a
saddle point (S). Enter the appropriate abbreviation for each question, or N if there is no critical point.
-3x²-4y²
= e
1. f(x, y)
Type of critical point:
2. f(x, y) = e³x²—4y²
Type of critical point:
3. f(x, y) = 3x² + 4y² + 4
Type of critical point:
4. f(x, y)
=
3x + 4y + 4
Type of critical point:
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